How to create a bridge loop without selecting face?
I believe the right question would be how to fill the gaps/holes.

While vertex selection does not work here to do it in one go, each side can be done without a problem, edge selection also works and in some situations avoids the unwanted face selection as well.

I made a video with what i believe you were looking for:



The Bridge loops tool would create new faces that would overlap 2 faces, the one mentioned in the question and one in the back. Even if you only bridge the top and front, you would close in the face mentioned in the picture, then it would be better to delete the face and bridge from the back to the front, spanning over the 3 edges in the back to the front 3 edges.

Like so: